The 19-year-old shot-stopper has had a wonderful season so far, and he has been given opportunities at club and international level, but Rhodes does not expect him to get carried away with the attention.
The Owls coach believes that Wildsmith's level-headed approach will stand him in good stead for the future, and puts him ahead of many other players of the same age.
“Joe doesn’t get too excited or too downbeat, whatever happens," Rhodes told the Sheffield Star. “His temperament is fantastic and that is why he’s looked so assured.
“He’s got to keep working at all aspects of his game but that is the same for every goalkeeper, whatever age.
“But you can’t buy his temperament. You see kids with all the talent in the world but they just don’t have the right mentality.”
Wildsmith has made five appearances for Wednesday's first team this season, and he was called into England's Under-21 squad for the first time this week.
His progress at Hillsborough and for the Three Lions highlights the potential that he has, and there are very high hopes for his future.
Wildsmith may struggle to break into Wednesday's first-choice starting line-up for the time being, though, as Keiren Westwood is so highly regarded.
Westwood has been one of the Owls' key players for over a year, and he is considered one of the best goalkeepers in the Championship.